On Sunday, January 1, 2017 at 10:10:48 AM UTC-5, mike wrote:
On 1/1/2017 3:57 AM, The Peeler wrote:
On Sat, 31 Dec 2016 23:12:26 -0800, mike wrote:

What's the dynamic if I pull down on it when it's cold outside?
Likely to break easier? It's about 2" diameter where I'd like it
to break.

No, I don't know what kind of tree it is. Some version of
maple, maybe...no leaves on it now. It's not in particularly
good health. Lots of decay.

Is there anything interesting I can do without hurting myself?

Don't break it, cut it.

https://www.amazon.com/High-Limb-CS-48-Rope-and-Chain -Saw/dp/B0000AX849

Turns out that I have one of those. Never got it to do anything.
Pulling down on the rope just digs the cutter into the wood and bends
the branch.

Depending on how high you can climb on your ladder, you could also get a
telescope pruner (cutter) with an attached saw blade (the cheap ones break
easily, though). You would only need to cut deep enough so you can break
the branch with your rope afterwards at the desired spot. And if the branch
should hang down loosely and the saw perhaps not work then, you could cut
through the remaining part with the pruner.

OK guys,
I have the rope saw...useless. I have a chainsaw on the end of an
extension pole...too short.
I have a ladder that I could probably rig to climb high enough.
BUT, the risk of injury is way too high to attempt such a feat.
I'd like to keep my feet firmly on the ground.

Let's get back to the question.

It's not "the question" (singular) it's the question*s* (plural).

If it's 18F outside, does the limb get more brittle enough to facilitate
just pulling it down? That's all I want to know.

That is not "all you want to know". Go back and read the last line of your
OP. Never mind, I'll paste it here for you:

"Is there anything interesting I can do without hurting myself?"

If that is not an invitation to offer suggestions unrelated to the
ambient temperature I don't know what is.